Problem: Solve for $n$. $2-2n=3n+17$ $n=$
Answer: We need to manipulate the equation to get $ n $ by itself. $\begin{aligned} 2-2n&=3n+17 \\\\ 2-2n {-3n} &= 3n+17{-3n} &&\gray{\text{Subtract 3n from each side.}}\\\\ -5n+2&=17 &&\gray{\text{Combine like terms.}}\\\\ -5n+2{-2} &= 17{-2} &&\gray{\text{Subtract 2 from each side.}}\\\\ -5n &=15 &&\gray{\text{Combine like terms.}}\\\\ \dfrac{-5n}{{-5}} &= \dfrac{15}{{-5}} &&\gray{\text{Divide each side by -5.}}\\\\ n &= {-3} &&\gray{\text{Simplify.}}\\\\ \end{aligned}$ The answer: $ n= { -3 }~~~~~~~~$ [Let's check our work!]